Bayesian network and linear regression methods have been widely applied to reconstruct cellular regulatory networks. In this work, we propose a Bayesian model averaging for linear regression (BMALR) method to infer molecular interactions in biological systems. This method uses a new closed form solution to compute the posterior probabilities of the edges from regulators to the target gene within a hybrid framework of Bayesian model averaging and linear regression methods. We have assessed the performance of BMALR by benchmarking on both in silico DREAM datasets and real experimental datasets. The results show that BMALR achieves both high prediction accuracy and high computational efficiency across different benchmarks. A pre-processing of the datasets with the log transformation can further improve the performance of BMALR, leading to a new top overall performance. In addition, BMALR can achieve robust high performance in community predictions when it is combined with other competing methods. The proposed method BMALR is competitive compared to the existing network inference methods. Therefore, BMALR will be useful to infer regulatory interactions in biological networks. A free open source software tool for the BMALR algorithm is available at https://sites.google.com/site/bmalr4netinfer/.